Hey there, I would like to begin by saying that it sounds to me that you are simply confused with your sexuality. There is nothing sick about this and people go through this every day. Identity crisis's are fairly common [even among people whom aren't homosexual] so you are going to be okay. I'm sure if I were your sister, though; I would feel a bit uncomfortable if I discovered my brother was wearing my undergarments and dresses. Perhaps you should purchase your own cross-dressing attire. Everyone has their own unique fetish.
Save up some money and go to a thrift shop. You are less likely to A) see anyone that you know, and B) have anyone care to question. Just go purchase your own private stock of clothing to wear when no one else is home.
What happens if you're caught?
Well then you are caught. Maybe that would be a good time to be open with both others and yourself. If you really don't want anyone else but the person who has caught you to know about your past time, sit him/her down and explain how important it is that it remains a secret. If they love you; they should understand and comply to your feelings.
Do you think that you could possibily be honest with your family about this? If you are willing to be up front and admit that you enjoy cross-dressing this would immediately get the shock factor out of the way. After all, how would you rather your family find out
Come home to their son/brother dressed in women's clothing
Be sat down and have things explained to them by their son/brother. It all really is up to what you are comfortable with, though.
I'm sure that there are support sites open for people with simaler fears as yours. You should google some cross-dressing forums and see what other people with this same fetish have to say to you about it. After all, the best advice comes from those who are actually in the situation.
If you really don't feel comfortable opening up to your family; you should consider only cross-dressing in the privacy of a place you know they will not be.
I hope everything works out for you.
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Antidisestablishmentarianism.